0554126 - ÚI 2022 RIV NL eng C - Konferenční příspěvek (zahraniční konf.)
Piga, S. - Sanhueza-Matamala, Nicolás
Codegree conditions for cycle decompositions and Euler tours in 3-uniform hypergraphs.
Procedia Computer Science. Vol. 195. Amsterdam: Elsevier, 2021 - (Ferreira, C.; Lee, O.; Miyazawa, F.), s. 350-358. ISSN 1877-0509.
[LAGOS 2021: Latin and American Algorithms, Graphs and Optimization Symposium /11./. Sao Paulo (BR), 17.05.2021-21.05.2021]
Grant CEP: GA ČR(CZ) GA19-08740S
Institucionální podpora: RVO:67985807
Klíčová slova: Cycles * Decompositions * Euler tours * Hypergraphs
Obor OECD: Pure mathematics
http://dx.doi.org/10.1016/j.procs.2021.11.043

We show that 3-graphs whose codegree is at least (2/3 + o(1))n can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to the o(1) term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn and Osthus.
Trvalý link: http://hdl.handle.net/11104/0328760